The invariant polynomials degrees of the Kronecker sum of two linear operators and additive theory

Abstract

Let G be an abelian group. Let A and B be finite non-empty subsets of G. By A+B we denote the set of all elements a+b with a[set membership, variant]A and b[set membership, variant]B. For c[set membership, variant]A+B, [nu]c(A,B) is the cardinality of the set of pairs (a,b) such that a+b=c. We call [nu]c(A,B) the multiplicity of c (in A+B).